Given the function f (x) = ax-b / x-2lnx, f (1) = 0, Given the function f (x) = ax-b / x-2lnx, f (1) = 0 (1) If the function f (x) is a monotone function in its domain of definition, the value range of real number a is obtained (2) The slope of the tangent line of the image at x = 1 is 0, a (n + 1) = f '(1 / an + 1) - Nan + 1. If A1 > = 3, it is proved that an > = n + 2

Given the function f (x) = ax-b / x-2lnx, f (1) = 0, Given the function f (x) = ax-b / x-2lnx, f (1) = 0 (1) If the function f (x) is a monotone function in its domain of definition, the value range of real number a is obtained (2) The slope of the tangent line of the image at x = 1 is 0, a (n + 1) = f '(1 / an + 1) - Nan + 1. If A1 > = 3, it is proved that an > = n + 2

1 f (1) = A-B = 0, a = B  f (x) = ax-a / x-2lnx f '(x) = a + A / x ^ 2-2 / x = (AX ^ 2-2x + a) / x ^ 2. According to the definition field, X ≠ 0, x ^ 2 ≠ 0, make (- 2) ^ 2-4a ^ 21 or A0 monotonically increasing, f' (1 / an + 1) = [(1 / an) · (an + 1)] ^ 2 = [1 + 1 / an] ^ 2  a (n + 1) = f '(1 / an + 1) - Nan + 1 = [1 + 1 / an